Derivatives The Power Rule

Front

What is the Power Rule for derivatives?

Back

The Power Rule states that if f(x) = x^n, then the derivative f'(x) = n*x^(n-1).

Front

Find the derivative of f(x) = 5x^3.

Back

f'(x) = 15x^2.

Front

Find the derivative of f(x) = 7x^4 - 2x^2 + 3.

Back

f'(x) = 28x^3 - 4x.

Front

What is the derivative of a constant?

Back

The derivative of a constant is 0.

Front

Find the derivative of f(x) = x^5.

Back

f'(x) = 5x^4.

Front

Find the derivative of f(x) = 2x^3 + 4x^2 - x + 1.

Back

f'(x) = 6x^2 + 8x - 1.

Front

Find the derivative of f(x) = 3x^2 + 2x + 1.

Back

f'(x) = 6x + 2.

Front

Find the derivative of f(x) = 4x^4 - 3x^3 - 9.

Back

f'(x) = 16x^3 - 9x^2.

Front

Find the derivative of f(x) = e^(3x+1).

Back

f'(x) = 3e^(3x+1).

Front

Find the derivative of f(x) = 2x^2(3x - 4).

Back

f'(x) = 18x^2 - 16x.